A child is hanging at the midpoint of a string and the string form an angle of 15 degrees with horizontal line. What's the force in the string? The answer is 850N. Who can show me the solution???
To calculate the force in the string, we need to consider the equilibrium of forces acting on the hanging child.
First, we need to understand that the downward force acting on the child due to gravity is equal to the weight of the child. We'll assume this weight is W.
Since the child is hanging at the midpoint of the string and the string forms an angle of 15 degrees with the horizontal line, we can draw a right triangle to represent the situation.
Now, let's break down the forces acting on the child. We have two components of the weight: the vertical component, which is acting downward, and the horizontal component, which is acting towards the center of the circle.
1. The vertical component of the weight (Wv) can be calculated using trigonometric functions. In this case, we can use the sine function:
Wv = W * sin(15°)
2. The horizontal component of the weight (Wh) can be obtained similarly, using the cosine function:
Wh = W * cos(15°)
Since the child is in equilibrium, the tension in the string (T) must balance the vertical component of the weight (Wv).
Therefore, T = Wv = W * sin(15°)
Given that the force in the string is 850N, we can set up an equation using the known value:
850N = W * sin(15°)
To solve for W, divide both sides of the equation by sin(15°):
W = 850N / sin(15°) ≈ 1972N
So, the weight of the child is approximately 1972N.
Note: In this explanation, we assumed there are no other forces acting on the child, such as air resistance or friction forces.